Geotechnical Engineering

DHARM

COMPRESSIBILITY AND CONSOLIDATION OF SOILS 221

If the samples were to be hermetically sealed, permitting no escape of water, the condi-

tions mentioned above would continue indefinitely. But, in the laboratory oedometer sample,

the porous stone disks tend to promptly eliminate the hydrostatic excess pressure at the top

and bottom of the sample creating a high gradient of pressure and consequent rapid drainage.

Gradually the void ratio decreases, as the hydrostatic excess pressure dissipates and the effec-

tive or intergranular pressure increases; this process is in a more advance state near the

drainage ends at the top and bottom than at the centre of the sample. The sample is said to be

“consolidating” under the stress increase ()σσ 21 −. This continues until the void ratio at all

points becomes e 2. Theoretically, no more water is forced out when the hydrostatic excess

pressure becomes zero; the effective pressure in the soil skeleton is σ 2 , and the sample is said

to have been “consolidated” under the pressure σ 2. It should be noted that “Consolidation” is a

relative term, which refers to the degree to which that the gradual process has advanced, and

does not refer to the stiffness of the material.

In fact, a quantitative idea of the consolidation or the ‘Degree of consolidation’ may be

obtained by what is called the ‘Consolidation ratio’, Uz.

Uz =

()

()

ee

ee

1

12

−

− ...(Eq. 7.15)

with reference to Fig. 7.18; this is the fundamental definition for Uz.
Usually it is expressed as per cent and is referred to as the ‘Per cent consolidation’. It
can be shown from Fig. 7.18 that Uz may also be written as follows:

Uz =

ee

ee

u

ui

1

12

1

21

1

−

−

= −

−

F

HG

I

KJ

σσ=−

σσ ...(Eq. 7.16)

in view of the relationship σσ 21 =+=+uui σ, from the same figure.

A mechanistic model for the phenomenon of consolidation was given by Taylor (1948),
by which the process can be better understood. This model, with slight modifications, is pre-
sented in Fig. 7.19 and is explained below:
A spring of initial height Hi is surrounded by water in a cylinder. The spring is analo-
gous to the soil skeleton and the water to the pore water. The cylinder is fitted with a piston of
area A through which a certain load may be transmitted to the system representing a satu-
rated soil. The piston, in turn, is fitted with a vent, and a valve by which the vent may be
opened or closed.

Referring to Fig. 7.19 (a), let a load P be applied on the piston. Let us assume that the
valve of the vent is open and no flow is occurring. This indicates that the system is in equilib-
rium under the total stress P/A which is fully borne by the spring, the pressure in the water
being zero.
Referring to Fig. 7.19 (b), let us apply an increment of load δP to the piston, the valve
being kept closed. Since no water is allowed to flow out, the piston cannot move downwards
and compress the spring; therefore, the spring carries the earlier stress of P/A, while the water
is forced to carry the additional stress of δP/A imposed on the system, the sum counteracting
the total stress imposed. This additional stress δP/A in the water in known as the hydrostatic
excess pressure.
Referring to Fig. 7.19 (c), let us open the valve and start reckoning time from that in-
stant. Water just starts to flow under the pressure gradient between it and the atmosphere
seeking to return to its equilibrium or atmospheric pressure. The excess pore pressure begins